The World Cup heralded misery for Liverpool’s forward line this summer, even the one not involved. Philippe Coutinho told a Brazilian radio station on Saturday that he was smarting at his omission from Luiz Felipe Scolari’s squad but vowed: “to use this anger and push myself to my limits.” To borrow a phrase from Dr David Banner, Liverpool’s rivals will not like Coutinho when he is angry on the evidence of this eye-catching defeat of Borussia Dortmund.

Coutinho received a standing ovation when replaced by Jordan Ibe in the 72nd minute at Anfield and with some justification. The gifted Brazilian was inspired against Jürgen Klopp’s side, creating the opening goal for Daniel Sturridge with a sublime touch, scoring the third and reassuring the Liverpool faithful that quick thinking, telepathy and glorious creativity has not disappeared from the team along with Luis Suárez. Only a friendly, of course, but Dortmund were demolished in some style. For Brendan Rodgers, the scoreline was secondary to the performance and the impact of a few debutants.

“I see Coutinho becoming a big talent in world football over the next four or five years for Liverpool and Brazil,” said the Liverpool manager, who revealed earlier this summer that the Brazilian is to be offered a new contract at Anfield.

“He is a magical operator. He came into this country and lit it up with his quality and now he has an opportunity this season to do it on a big stage in the Champions League. It is about sustaining his level on the big stage now. I’m sure he will. He is so gifted and his ability to get out of tight situations, his view of the game, is magical.”

Angry Coutinho and the maturing Raheem Sterling were in devastating form ahead of the Premier League opener against Southampton and Liverpool’s creative threat will be supplemented this season by Lazar Markovic and Adam Lallana, the two new signings missing here through injury. Daniel Agger was absent too, though Rodgers claimed that was for fitness reasons. “We haven’t had any inquiries for Daniel,” he said.

New boys also impressed for Liverpool, Dejan Lovren especially. The £20m signing from Southampton was one of three summer additions to start against Dortmund, the right-back Javier Manquillo and the central midfielder Emre Can the others, and instantly caught the eye with his strength, aerial presence and accurate left foot. The watching Southampton coaching duo of Ronald Koeman and Sammy Lee received an unnecessary reminder of what they have lost.

“I was really pleased with all the new signings,” Rodgers added. “Dejan is perfect, exactly what we have been looking for since Jamie Carragher retired; a dominant, No1 centre-half who reads the game really well. You also saw his good range of passing with right and left foot. I thought Manquillo was outstanding too. He is only 19 and it was his first game at Anfield. He is the type of full-back I like; he gets tight to people, stops crosses coming in and has the energy to get forward.”

Lovren dominated Dortmund striker Adrián Ramos, the Colombia international who was signed from Hertha Berlin to try and compensate for Robert Lewandowski along with Ciro Immobile, the leading goalscorer in Serie A last season with Torino. The Croatian defender won every aerial challenge against the tall Ramos and helped instigate a comfortable victory by assisting in the opening goal on 10 minutes.

The central defender picked out Coutinho in space deep inside the Germans’ half and the Brazilian put Sturridge clear with an exquisite flick over the Dortmund rearguard. Sturridge had time to pick his spot and finished low into Mitchell Langerak’s far corner. Three minutes later it was two when Lovren showed he will add to Liverpool’s already consistent threat at set-pieces by powering home a far post header from a Steven Gerrard corner.

Dortmund are a fortnight away from the start of the new Bundesliga season and started without their German World Cup winners but that was no excuse for Klopp, who appeared on the touchline in a garish yellow baseball cap to berate his players. Yet last season’s league and cup runners-up in Germany could not contain the outstanding combinations between Coutinho, Sterling and Sturridge, who showed that, while a world class piece of last season’s forward line has gone, Liverpool’s incisive style under Rodgers will remain.

Sterling has shone throughout pre-season and his increasing maturity was on display as he issued tactical instructions to Can, then showed his strength to knock the colossal Dortmund captain Sebastian Kehl off the ball with a shoulder charge. The England winger seized on a loose pass across the Dortmund defence to create the third for Coutinho with a fine pass that Liverpool’s No10 slipped into the far corner from an acute angle.

The fourth followed a mesmerising Liverpool attack that had appeared to break down when Sturridge failed to connect with Coutinho’s pass, only to retrieve a seemingly lost cause and set-up Jordan Henderson for a tap-in.